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det - a(1 i,j a(2 i,j then det A = det A 1 det A 2 where A...

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Properties of Determinants Given a square matrix A the determinant, det A , of A has the following properties: 1. If any row or column of A has only zero entries, then det A = 0. 2. det A = det A . 3. If a row or column of a matrix is multiplied by a constant, k , then the value of the determinant is k det A . 4. If two rows or two columns of the matrix A are interchanged, the value of the determinant is - 1 det A . 5. If two rows or two columns of the matrix are proportional then det A = 0. 6. If each element a i,j of the i th row (or j th column) can be written in the form
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Unformatted text preview: a (1) i,j + a (2) i,j , then det A = det A 1 + det A 2 where A 1 is the matrix derived by replacing the i th row (or j th column) with a (1) i,j and A 2 that derived by replacing the i th row (or j th column) by a (2) i,j . 7. The addition of a multiple of a row (or column) of a determinant to another row (or column) of the determinant leaves the value of the determinant unchanged. 8. Let A and B be two n × n matrices. Then det( AB ) = det A det B ....
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